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POVectorized computation of 3-point correlation functions in Matlab?
 

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  1. POVectorized computation of 3-point correlation functions in Matlab?
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    <p>I would like to compute the 2- and 3-point correlation functions R2, R3 of samples of a vector by appropriate histogramming of the elements of a vector (num_samples samples of length system_size), and the corresponding cluster functions T2, T3. For simplicity I am considering histogramming across uniform bins.</p> <p>What is a good way to vectorize and/or speed up the following code?</p> <pre><code>n = length(mesh); R2 = zeros(n, n); R3 = zeros(n, n, n); for sample_id=1:num_samples s = samples(:, sample_id); d = mesh(2) - mesh(1); % Which bin does the ith sample s belong to? bins = ceil((s - mesh(1))/d); % Compute two-point correlation function for i = 1:system_size for j = 1:system_size if i ~= j R2(bins(i), bins(j))=R2(bins(i), bins(j))+1; end end end % Compute three-point correlation function for i = 1:system_size for j = 1:system_size if i ~= j for k = 1:system_size if k ~= j &amp;&amp; k ~= i R3(bins(i), bins(j), bins(k))=R3(bins(i), bins(j), bins(k))+1; T3(x1, x2, x3) = R3(x1,x2,x3)-R1(x1)*R2(x2,x3)-R1(x2)*R2(x1,x3)... -R1(x3)*R2(x1,x2)+2*R1(x1)*R1(x2)*R1(x3); end end end end end end R2 = R2/sum(R2(:)); R3 = R3/sum(R3(:)); T3 = zeros(n, n, n); % Compute three-point cluster function for i = 1:n for j = 1:n if i ~= j for k = 1:n if k ~= j &amp;&amp; k ~= i T3(x1, x2, x3) = R3(x1,x2,x3)-R1(x1)*R2(x2,x3)-R1(x2)*R2(x1,x3)... -R1(x3)*R2(x1,x2)+2*R1(x1)*R1(x2)*R1(x3); end end end end end </code></pre> <p>Naively I thought hist3(bins, bins...) or crosstab(bins, bins) would almost do what I want, which is to look for correlated occurrences of elements of the vector, but it doesn't.</p> <hr> <p>Example:</p> <p>If my inputs within the outermost loop are </p> <pre><code>s = [1.2 3.1 4.6 4.7 5.1] mesh = 0:0.5:6 </code></pre> <p>then the quantized data should be</p> <pre><code>bins = [3 7 10 10 11] </code></pre> <p>and R2 should be</p> <pre><code>&gt;&gt; R2 R2 = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 2 0 0 0 1 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 </code></pre>
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